In a real atom, each electron is effectively a cloud of charge and current, not changing in time. Think of water flowing smoothly over a rock, forming a stationary wave. If the flow is irregular, it will lead to waves spreading in all directions; but if it is perfectly smooth, it will not. The water flows, accelerates, and decelerates, but does not cause spreading waves.
Here is a more direct way to think about it. Electrons do not act like point charges in their orbitals. In fact, they act like a continuous distribution of charge and current that does not change with time. By analogy: Suppose you have a superconductive ring hanging in space, carrying a constant current. At each point in the ring, the electrons are accelerating because the direction of their motion is changing. But the distribution of current and charge is constant. That is why the ring will not radiate electromagnetic waves. However, if a single charged particle moved around a ring-shaped path it would radiate, because the distribution of current and charge in that case would not be constant.
It is incorrect to say that electrons move around the nucleus of an atom with constant velocity; they don't. The farther they are from the nucleus, the slower the effective velocity is; and the closer they are the faster it is. It's true that stationary charge/current distributions do not radiate, but "stationary" does not mean that nothing is going on: there is still a continuous distribution of what amounts to accelerating and decelerating charge motion. But because that distribution does not change in time, there is no radiation.
The bottom line answer to your question: A Rutherford atom, with point electrons orbiting a nucleus, would indeed radiate electromagnetic radiation. But Rutherford atoms do not exist.